Multiscale Approach to Understand the Multiphysics Phenomena in Bone Adaptation - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 44

Fig. 4 Equilibrium
electrostatic potential in an
electrolyte solution bordered
by a plane negative surface
(reproduced with permission
from [ 115 ]). The
microstructure of the ionic
distribution at the interface
induces the phenomenon of
Debye shielding by the ion
cloud of the opposite sign
(double layer phenomenon)
Even if highly studied in the 1980s to prove the lacuno-canalicular fluid
movement thanks to the stress-generated streaming potentials [ 123 , 138 , 139 ],
these hydro-electro-chemical couplings have been poorly studied in the context of
the flow induced mechano-transduction.
Additionally, some ionic exchanges appear between the bone matrix and the
bone fluid [ 33 , 91 ] as well as between bone cells and the interstitial fluid. Indeed,
being living entities, bone cells receive nutrients, throw their waste and commu-
nicate with one another through the interstitial fluid [ 100 ]. This biochemical
activity and the surface chemical reactions lead to a change of the physico-
chemical properties of the fluid/solid interface. In particular, the negative surface
charge density is modified when exchanging ionic species and thus depends on the
ionic concentration [ 146 ]. Because of the electro-viscous couplings, these
exchanges influence the interstitial fluid transport [ 76 , 80 ] and, in fine, the fluid
mechano-transduction signals.
2.5.3 Multiphysics Mechano-Transduction of Bone Remodelling:
A Multiscale Strategy
Here, we propose to adopt a fresh new angle to elucidate the multiphysics con-
sequences on the mechano-transduction of bone remodelling. Indeed, combining a
description of electrokinetics in bone tissue [ 84 - 86 ] with the description of piezo-
biomaterials [ 99 ], we intend to derive a fully coupled electro-hydro-mechanical
model of bone tissue [ 74 ]. Since the anatomical origin of bone electricity is located
at the microscopical scale, our electro-chemo-mechanical description combines
the collagen fibers deformation effects and the advection of ionic double layers
through canalicular network. Then, adopting the periodic asymptotic homogeni-
zation procedure proposed by Auriault and Sanchez-Palencia [ 8 ] based on the